Probing the Effects of Lorentz-Symmetry Violating Chern-Simons and Ricci-Cotton Terms in Higher Derivative Gravity

Abstract

The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of operators that splits the fundamental fields according to their individual degrees of freedom. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes gets a new insight. Our conclusion is that the only tachyon- and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a time-like vector of the type $v^{\mu }=(\mu ,\vec{0})$. Spectral consistency imposes taht the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to usual gauge theories whenever conditions for suppression of tachyons and ghosts are required.

15 pages. It coincides with the version published in Phys. Rev. D

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• Lorentz violation and higher-derivative gravity
• New class of spin projection operators for 3D models
• Considerations on the Graviton Excitation Modes of Horava-Lifshitz Gravity
• Semi-transparent boundaries in CPT-even Lorentz violating electrodynamics
• Towards Constraining Parity-Violations in Gravity with Satellite Gradiometry
• Critical gravity in the Chern-Simons modified gravity
• Unimodular gravity theory with external sources in a Lorentz-symmetry breaking scenario